3X^2+X-7=4X

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Solution for 3X^2+X-7=4X equation: 


Simplifying
3X2 + X + -7 = 4X

Reorder the terms:
-7 + X + 3X2 = 4X

Solving
-7 + X + 3X2 = 4X

Solving for variable 'X'.

Reorder the terms:
-7 + X + -4X + 3X2 = 4X + -4X

Combine like terms: X + -4X = -3X
-7 + -3X + 3X2 = 4X + -4X

Combine like terms: 4X + -4X = 0
-7 + -3X + 3X2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-2.333333333 + -1X + X2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + -1X + 2.333333333 + X2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + -1X + X2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -1X + X2 = 0 + 2.333333333
-1X + X2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
-1X + X2 = 2.333333333

The X term is -1X.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1X + 0.25 + X2 = 2.333333333 + 0.25

Reorder the terms:
0.25 + -1X + X2 = 2.333333333 + 0.25

Combine like terms: 2.333333333 + 0.25 = 2.583333333
0.25 + -1X + X2 = 2.583333333

Factor a perfect square on the left side:
(X + -0.5)(X + -0.5) = 2.583333333

Calculate the square root of the right side: 1.607275127

Break this problem into two subproblems by setting 
(X + -0.5) equal to 1.607275127 and -1.607275127.


Subproblem 1
X + -0.5 = 1.607275127

Simplifying
X + -0.5 = 1.607275127

Reorder the terms:
-0.5 + X = 1.607275127

Solving
-0.5 + X = 1.607275127

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

Add '0.5' to each side of the equation.
-0.5 + 0.5 + X = 1.607275127 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + X = 1.607275127 + 0.5
X = 1.607275127 + 0.5

Combine like terms: 1.607275127 + 0.5 = 2.107275127
X = 2.107275127

Simplifying
X = 2.107275127


Subproblem 2
X + -0.5 = -1.607275127

Simplifying
X + -0.5 = -1.607275127

Reorder the terms:
-0.5 + X = -1.607275127

Solving
-0.5 + X = -1.607275127

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

Add '0.5' to each side of the equation.
-0.5 + 0.5 + X = -1.607275127 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + X = -1.607275127 + 0.5
X = -1.607275127 + 0.5

Combine like terms: -1.607275127 + 0.5 = -1.107275127
X = -1.107275127

Simplifying
X = -1.107275127


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {2.107275127, -1.107275127}

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